I was browsing for other information, but came across this thread and just wanted to drop in some details regarding batteries. There's some great information on here already, but I just had a few points make :-)
The voltage difference between the 10.8 and the 11.1 batteries is negligable on any laptop. There are changes in voltage in 'all' batteries as a natural part of what they are, but beyond that, batteries drop in power anyway as they discharge and only the circuit they are fitted to will decide if it's flat or not enough to work it (until the battery just cannot work any longer).
How does any laptop know the battery is going flat? It tests voltage, amd when it finds it's getting too low, it shuts down (or just goes off without warning - that's it's 2nd layer of auto-off, 1st level is a warning with OS shut down, 2nd level is full off to avoid lower voltage causing data problems while reading/writing. To leave a circuit on a laptop struggling on a low battery with (for example) 7 volts, could cause all kinds of data corruption, so the best thing is just instant off - then it's far more likely to just stop what it's doing.
Losing power slowly could cause a hard drive to smear data (in theory) across a drives platter ARRGGGHHH disaster!
It had been mentioned here about voltages on laptops being 19v, so why is that? Well this isn't mentioned much but is important to realise....
No circuit uses 19 volts. Check on components and you instantly see 1v, 3v, 5v 9v, 12v etc. Now where does your 19v laptop fit in then?
Well its for power and safety - no laptop uses more than 12v, and most voltages are 5v, or lower like 1.3 for CPU's and things like RAM. If that 12v part needs power and your charger was 12v, you'd be straining the whole circuit - that's no good. So you have 19 volts, to power the 12's, and the 5's, and the other lower voltage parts, and also, of course, that all important trickle charge to the battery (usually between 1.5 and 3.5 volts to charge things with, 3.5 being Fast Chargers - not used on laptops).
The bit to note is, all the voltages are 'nearly' things. None of it is precise at this level, only things like RAM, data lines and CPU/GPU have 100% precision on voltages. The rule on such techinical circuits is - always have a little more power than you need just in case, but always have a protected voltage level anyway.
Consider the old fashioned and well used 7805 voltage regulator - you can slap 35+ volts into them, and the just casually give you 5volts output and laugh while doing it. That's your circuit protection from high voltages right there.
Laptops, both battery and mainboard, all have more modern versions of the same kind of thing inside them.
And also, I happily put 11.1 or 14.4 batteries in several makes of laptops without any difference or problem. As an example, I have here on my desk a Packard Bell MIT-SABLE-C, that happily uses either voltage, and I have 6 batteries I've been testing on it, All do the same thing, because the higher voltage battery has less amp, so the power level at the end all stays about the same.